/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(29 + -27 * Arg_0 + -27 * Arg_1, 2 + -27 * Arg_0 + 27 * Arg_2, 29 + -27 * Arg_0 + -27 * Arg_3, 29)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 242 ms]
(2) BOUNDS(1, max(29 + -27 * Arg_0 + -27 * Arg_1, 2 + -27 * Arg_0 + 27 * Arg_2, 29 + -27 * Arg_0 + -27 * Arg_3, 29))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
l0(A, B, C, D) -> Com_1(l1(A, B, C, D)) :|: TRUE
l1(A, B, C, D) -> Com_1(l1(A + A + B, C, C + 1, D)) :|: A + B >= 0 && A <= D

The start-symbols are:[l0_4]


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(1) Koat2 Proof (FINISHED)
YES( ?, 2+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]) {O(n)})



Initial Complexity Problem:

  Start:  l0  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3  

  Temp_Vars:    

  Locations:  l0, l1  

  Transitions:

  0: l0->l1

  1: l1->l1  



Timebounds: 

  Overall timebound: 2+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]) {O(n)}

  0: l0->l1: 1 {O(1)}

  1: l1->l1: 1+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]) {O(n)}



Costbounds:

  Overall costbound: 2+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]) {O(n)}

  0: l0->l1: 1 {O(1)}

  1: l1->l1: 1+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]) {O(n)}



Sizebounds:

`Lower:

  0: l0->l1, Arg_0: Arg_0 {O(n)}

  0: l0->l1, Arg_1: Arg_1 {O(n)}

  0: l0->l1, Arg_2: Arg_2 {O(n)}

  0: l0->l1, Arg_3: Arg_3 {O(n)}

  1: l1->l1, Arg_1: Arg_3 {O(n)}

  1: l1->l1, Arg_2: Arg_2 {O(n)}

  1: l1->l1, Arg_3: Arg_3 {O(n)}

`Upper:

  0: l0->l1, Arg_0: Arg_0 {O(n)}

  0: l0->l1, Arg_1: Arg_1 {O(n)}

  0: l0->l1, Arg_2: Arg_2 {O(n)}

  0: l0->l1, Arg_3: Arg_3 {O(n)}

  1: l1->l1, Arg_0: 2^(1+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]))*((1+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]))*max([0, max([Arg_1, max([Arg_3, 1+Arg_3+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])])])])])+max([0, max([Arg_3, max([Arg_0, max([Arg_1, 1+Arg_3+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])])])])])])) {O(EXP)}

  1: l1->l1, Arg_1: max([Arg_3, 1+Arg_3+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])])]) {O(n)}

  1: l1->l1, Arg_2: Arg_2 {O(n)}

  1: l1->l1, Arg_3: 1+Arg_3+27*max([1, max([1+-(Arg_3)-Arg_0, max([1+-(Arg_1)-Arg_0, Arg_2-Arg_0])])]) {O(n)}


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(2)
BOUNDS(1, max(29 + -27 * Arg_0 + -27 * Arg_1, 2 + -27 * Arg_0 + 27 * Arg_2, 29 + -27 * Arg_0 + -27 * Arg_3, 29))